Homework Help: Energy considerations in LC oscillations. How is it in SHM?

1. Jan 7, 2009

weirdo

1. The problem statement, all variables and given/known data
Hi

When you set up an LC (tank) circuit there is oscillation due to charge and discharge of capactor and storage of energy in the inductor.

How do you prove that it is simple harmonic? And also how do you prove (mathematically) energy is conserved in an undamped LC oscillation?

2. Relevant equations
For C: emf= q/c
For L: emf= -L (dI/dt)

3. The attempt at a solution
emf across C=emf across L
ie, q/c + L (dI/dt) = 0

2. Jan 7, 2009

LennoxLewis

By setting up an equation of the voltage, using the relevant formulas you've already given, you come to a second order differential equation that, outside of different constants, is equivalent to the second order DE of the harmonic oscillator.

3. Jan 7, 2009

weirdo

Fine thanks. I got the bit on proving it to be in SHM. How should I start to prove that total energy is conserved in a mathematical way?

I can say let at t=0s, energy of system in in C, E= 1/2 CV2 -->1
after 1/4 the time period, energy is fully in inductor, E= 1/2 LI2 --> 2

So Etotal = 1 + 2.

How do I show it is constant for undamped oscillations?